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Dynamical invariants and inverse period-doubling cascades in multi-delay systems. (English) Zbl 07867388

MSC:

34Kxx Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
37Dxx Dynamical systems with hyperbolic behavior
34Cxx Qualitative theory for ordinary differential equations

Software:

DDE-BIFTOOL
Full Text: DOI

References:

[1] Soriano, M. C.; García-Ojalvo, J.; Mirasso, C. R.; Fischer, I., Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers, Rev. Mod. Phys., 85, 421-470, 2013 · doi:10.1103/RevModPhys.85.421
[2] Petkoski, S.; Jirsa, V. K., Transmission time delays organize the brain network synchronization, Philos. Trans. R. Soc. A, 377, 20180132, 2019 · Zbl 1462.92022 · doi:10.1098/rsta.2018.0132
[3] Hutt, A.; Mierau, A.; Lefebvre, J., Dynamic control of synchronous activity in networks of spiking neurons, PLoS One, 11, e0161488, 2016 · doi:10.1371/journal.pone.0161488
[4] Milton, J.; Cabrera, J. L.; Ohira, T.; Tajima, S.; Tonosaki, Y.; Eurich, C. W.; Campbell, S. A., The time-delayed inverted pendulum: Implications for human balance control, Chaos, 19, 026110, 2009 · Zbl 1309.92020 · doi:10.1063/1.3141429
[5] Mensour, B.; Longtin, A., Chaos control in multistable delay-differential equations and their singular limit maps, Phys. Rev. E, 58, 410-422, 1998 · doi:10.1103/PhysRevE.58.410
[6] Foss, J.; Longtin, A.; Mensour, B.; Milton, J., Multistability and delayed recurrent loops, Phys. Rev. Lett., 76, 708-711, 1996 · doi:10.1103/PhysRevLett.76.708
[7] Losson, J.; Mackey, M. C.; Longtin, A., Solution multistability in first-order nonlinear differential delay equations, Chaos, 3, 167-176, 1993 · Zbl 1055.34510 · doi:10.1063/1.165982
[8] Appeltant, L.; Soriano, M. C.; Van Der Sande, G.; Danckaert, J.; Massar, S.; Dambre, J.; Schrauwen, B.; Mirasso, C. R.; Fischer, I., Information processing using a single dynamical node as complex system, Nat. Commun., 2, 468 · doi:10.1038/ncomms1476
[9] Penkovsky, B.; Porte, X.; Jacquot, M.; Larger, L.; Brunner, D., Coupled nonlinear delay systems as deep convolutional neural networks, Phys. Rev. Lett., 123, 054101, 2019 · doi:10.1103/PhysRevLett.123.054101
[10] Inubushi, M.; Yoshimura, K., Reservoir computing beyond memory-nonlinearity trade-off, Sci. Rep., 7, 10199, 2017 · doi:10.1038/s41598-017-10257-6
[11] Ahlborn, A.; Parlitz, U., Controlling dynamical systems using multiple delay feedback control, Phys. Rev. E, 72, 016206, 2005 · doi:10.1103/PhysRevE.72.016206
[12] Kiss, G.; Röst, G., Controlling Mackey-Glass chaos, Chaos, 27, 114321, 2017 · Zbl 1390.34195 · doi:10.1063/1.5006922
[13] Schöll, E.; Schuster, H. G., Handbook of Chaos Control, 2008, John Wiley & Sons · Zbl 1130.93001
[14] Coombes, S.; Laing, C., Delays in activity-based neural networks, Philos. Trans. R. Soc. A, 367, 1117-1129, 2009 · Zbl 1185.92003 · doi:10.1098/rsta.2008.0256
[15] Tavakoli, S. K.; Longtin, A., Multi-delay complexity collapse, Phys. Rev. Res., 2, 033485, 2020 · doi:10.1103/PhysRevResearch.2.033485
[16] Müller, D.; Otto, A.; Radons, G., Laminar chaos, Phys. Rev. Lett., 120, 084102, 2018 · doi:10.1103/PhysRevLett.120.084102
[17] Thiel, A.; Schwegler, H.; Eurich, C. W., Complex dynamics is abolished in delayed recurrent systems with distributed feedback times, Complexity, 8, 102-108, 2003 · doi:10.1002/cplx.10087
[18] Vicente, R.; Dauden, J.; Colet, P.; Toral, R., Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop, IEEE J. Quantum Electron., 41, 541-548, 2005 · doi:10.1109/JQE.2005.843606
[19] Doyne Farmer, J., Chaotic attractors of an infinite-dimensional dynamical system, Physica D, 4, 366-393, 1982 · Zbl 1194.37052 · doi:10.1016/0167-2789(82)90042-2
[20] Wernecke, H.; Sándor, B.; Gros, C., Phys. Rep., 824, 1-40, 2019 · doi:10.1016/j.physrep.2019.08.001
[21] Breda, D.; Schiava, S. D., Pseudospectral reduction to compute Lyapunov exponents of delay differential equations, Discrete Contin. Dyn. Syst. B, 23, 2727, 2018 · Zbl 1401.37091 · doi:10.3934/dcdsb.2018092
[22] Breda, D.; Maset, S.; Vermiglio, R., Stability of Linear Delay Differential Equations, 2015, Springer: Springer, New York · Zbl 1269.35012
[23] Pikovsky, A.; Politi, A., Lyapunov Exponents: A Tool to Explore Complex Dynamics, 2016, Cambridge University Press · Zbl 1419.37002
[24] Engelborghs, K.; Luzyanina, T.; Roose, D., Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL, ACM Trans. Math. Softw., 28, 1-21, 2002 · Zbl 1070.65556 · doi:10.1145/513001.513002
[25] Bandt, C.; Pompe, B., Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett., 88, 4, 2002 · doi:10.1103/PhysRevLett.88.174102
[26] Larger, L.; Lacourt, P.-A.; Poinsot, S.; Hanna, M., From flow to map in an experimental high-dimensional electro-optic nonlinear delay oscillator, Phys. Rev. Lett., 95, 043903, 2005 · doi:10.1103/PhysRevLett.95.043903
[27] Zunino, L.; Soriano, M. C.; Fischer, I.; Rosso, O. A.; Mirasso, C. R., Permutation-information-theory approach to unveil delay dynamics from time-series analysis, Phys. Rev. E, 82, 046212, 2010 · doi:10.1103/PhysRevE.82.046212
[28] Mensour, B.; Longtin, A., Power spectra and dynamical invariants for delay-differential and difference equations, Physica D, 113, 1-25, 1998 · Zbl 0935.34062 · doi:10.1016/S0167-2789(97)00185-1
[29] Erneux, T., Applied Delay Differential Equations, 2009, Springer-Verlag: Springer-Verlag, New York · Zbl 1201.34002
[30] Stepan, G., Retarded Dynamical Systems: Stability and Characteristic Functions, 1989, Longman: Longman, Harlow · Zbl 0686.34044
[31] Longtin, A., “Oscillation onset in neural delayed feedback,” in Advances in Neural Information Processing Systems 3 (NIPS 1990) (Morgan-Kaufmann, 1991), pp. 130-136.
[32] René, A.; Longtin, A., Mean, covariance, and effective dimension of stochastic distributed delay dynamics, Chaos, 27, 114322, 2017 · Zbl 1391.34132 · doi:10.1063/1.5007866
[33] Yanchuk, S.; Perlikowski, P., Delay and periodicity, Phys. Rev. E, 79, 046221, 2009 · doi:10.1103/PhysRevE.79.046221
[34] Longtin, A., Noise-induced transitions at a Hopf bifurcation in a first-order delay-differential equation, Phys. Rev. A, 44, 4801-4813, 1991 · doi:10.1103/PhysRevA.44.4801
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